Shortcut and exact doubling time side by side
The Rule of 72 is useful because it is fast, not because it is exact. This workspace keeps the shortcut and logarithmic annual-compounding result side by side, exposes approximation error and reverse-solves the Rule-of-72 rate for a target doubling period.
How to use this calculator
Enter a positive annual growth rate.
Optionally enter a target doubling period to reverse-solve the Rule-of-72 rate.
Compare the mental shortcut with the exact constant-rate annual-compounding result.
Where people use it
- •Quick compound-growth sanity checks
- •Teaching the Rule of 72
- •Comparing the shortcut with exact logarithmic doubling time
Example: 8% annual growth
The Rule of 72 estimates 9 years because 72 ÷ 8 = 9. The exact constant 8% annual-compounding doubling time is slightly different, which the calculator shows directly.
Keep the approximation in context
- •This is a mathematical growth illustration, not an investment-return forecast.
- •The exact comparison assumes a constant annual effective rate and annual compounding.
- •Taxes, fees, inflation and changing returns are not modeled.
Frequently asked questions
Why use 72?+
72 has many convenient divisors and gives a useful mental approximation across common growth rates.
Is the Rule of 72 exact?+
No. The exact constant-rate annual-compounding doubling time uses logarithms.
Can I find the rate needed to double in a target number of years?+
Yes. The reverse shortcut is 72 divided by the target years.
Semantic next steps
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Keep the result connected to the real job
MAXScanner keeps the formula and assumptions beside the result so you can verify the number before using it in a drawing, estimate, specification, worksheet or document. Where a supplier, manufacturer, drawing or applicable standard owns a requirement, that source remains authoritative.